x/x-1+x-1/x=17/4solved by middle term splitting and cross multiplication.
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x/x-1 + x-1/x=17/4
[x*x+(x-1)(x-1)] /(x-1)x = 17/4
x^2+x^2-x-x+1 /x^2-x=17/4
4(2x^2-2x+1)=17(x^2-x)
8x^2-8x+4=17x^2-17x
17x^2-8x^2-17x+8x-4=0
9x^2-9x-4=0
9x^2-12x+3x-4
3x(3x-4)+1(3x-4)
(3x-4) or (3x+1)
x=4/3 or x=-1/3
[x*x+(x-1)(x-1)] /(x-1)x = 17/4
x^2+x^2-x-x+1 /x^2-x=17/4
4(2x^2-2x+1)=17(x^2-x)
8x^2-8x+4=17x^2-17x
17x^2-8x^2-17x+8x-4=0
9x^2-9x-4=0
9x^2-12x+3x-4
3x(3x-4)+1(3x-4)
(3x-4) or (3x+1)
x=4/3 or x=-1/3
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